Quantum entanglement correlations in double quark PDFs

Methods from Quantum Information Theory are used to scrutinize quantum correlations encoded in the two-quark density matrix over light-cone momentum fractions <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>x</a:mi><a:mn>1</a:mn></a:msub></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>x</c:mi><c:mn>2</c:mn></c:msub></c:math>. A nonperturbative three quark model light-cone wavefunction predicts significant nonclassical correlations associated with the “entanglement negativity” measure for asymmetric and small quark momentum fractions. We perform one step of QCD scale evolution of the entire density matrix, not just its diagonal (dPDF), by computing collinearly divergent corrections due to the emission of a gluon. Finally, we present first qualitative numerical results for single-step scale evolution of quantum entanglement correlations in double quark PDFs. At a higher <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>Q</e:mi><e:mn>2</e:mn></e:msup></e:math> scale, the nonclassical correlations manifest in the dPDF for nearly symmetric momentum fractions.